Geodesic
On the compatibility of a~system of random comparisons
Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 75-85

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We consider a random graph whose each cycle is marked with a certain probability depending on the cycle length. The asymptotic behaviour of the probability of absence of non-marked cycles is described. As a corollary, the asymptotic behaviour of the probability of consistency of a system of random congruences modulo two with random non-equiprobable right-hand sides and also of a system with non-random right-hand sides is described. 
@article{DM_1992_4_3_a5,
     author = {V. F. Kolchin},
     title = {On the compatibility of a~system of random comparisons},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_3_a5/}
}
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V. F. Kolchin. On the compatibility of a~system of random comparisons. Diskretnaya Matematika, Tome 4 (1992) no. 3, pp. 75-85. http://geodesic.mathdoc.fr/item/DM_1992_4_3_a5/